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# PS Number property

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PS Number property [#permalink]  01 Apr 2009, 02:27
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Question Stats:

30% (01:51) correct 69% (00:55) wrong based on 2 sessions
20. If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?
Ⅰ. x = y
Ⅱ. y = 1
Ⅲ. x and y are prime integers.
(A) None
(B) Ⅰ only
(C) Ⅱonly
(D) Ⅲonly
(E) Ⅰand Ⅲ
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Re: Number property........... [#permalink]  01 Apr 2009, 02:47
good Q
Prime Integers are 2,3,5,7,11,13,............
IMO C

See, 3x/y is a prime integer greater than 2 say 3

hence That prime integer(3) will have 2 divisors-3 and x/y
hence x=y

is it from OG 12?

20. If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?
Ⅰ. x = y
Ⅱ. y = 1
Ⅲ. x and y are prime integers.
(A) None
(B) Ⅰ only
(C) Ⅱonly
(D) Ⅲonly
(E) Ⅰand Ⅲ
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Re: Number property........... [#permalink]  01 Apr 2009, 16:56
I got A.

You can pick numbers that contradict all three statements.
What is the OA?
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Re: ps Number property........... [#permalink]  02 Apr 2009, 15:44
A.

z=3x/y
for z to be prime number
x=10 y=6 I is not true

Y could be 1 where our question asks must be...

Prime number could be... with x/y 3/3, 15/15
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Re: ps Number property........... [#permalink]  02 Apr 2009, 23:33

3x/y = 3*(x/y) <- prime number that is greater than 2.
if x and y are equal than the eqn becomes 3 * (1) = 3 (prime number greater than 2)

Since we are looking for an integer (all prime numbers are integers) and y != 3 than x must equal y.
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Re: ps Number property........... [#permalink]  03 Apr 2009, 17:14
matrix777 wrote:

3x/y = 3*(x/y) <- prime number that is greater than 2.
if x and y are equal than the eqn becomes 3 * (1) = 3 (prime number greater than 2)

Since we are looking for an integer (all prime numbers are integers) and y != 3 than x must equal y.

Initially I fell for it but take x=14 and y =6 3x/y = 7 which is still a prime and x ! = y

Hence B is not correct.
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Re: ps Number property........... [#permalink]  06 Apr 2009, 17:42
The answer is A - Other than picking numbers, is there any option here ? I spent more than 2 minutes on this and fell for the wrong answer.

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Re: ps Number property........... [#permalink]  08 Apr 2009, 05:36
take x=10 and y=6 and hence the answer is A.
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Re: ps Number property........... [#permalink]  07 May 2009, 21:22
Ans must be B

3x/y and if x=y then ans is 3 and 3 is prime number, which is greater than 2. so ans must be B. Please post OA.
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Re: PS Number property [#permalink]  12 Oct 2009, 08:38
(3x/y) is a prime integer greater than 2. which of the following must be true

Suppose P=3x/y

Possible values of P = 3,5,7,11 ......

Statement I:
If P = 3 , x=y TRUE
If P = 5, x=y FALSE <== Statement I is not always correct

Statement II:
If y=1 is TRUE => P = 3x
Since P is a prime number, it cannot be a multiple of 3

Statement III:
suppose x = 7 and y=5 , P= 21/5 => Not a prime number
You can fill some other values of x and y

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Re: PS Number property [#permalink]  12 Oct 2009, 11:49
If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?
Ⅰ. x = y
Ⅱ. y = 1
Ⅲ. x and y are prime integers.
(A) None
(B) Ⅰ only
(C) Ⅱonly
(D) Ⅲonly
(E) Ⅰand Ⅲ

Answer to this question is A. None of the statements (I,II,III) must be true.

This Q. can be solved by number plugging in a minute but it's quite tricky, so let's generalize it so to understand the concept, as there are many similar problems in GMAT:

Q. says that: y≠3 and that 3x/y IS a prime integer. Then it asks which of the statements MUST be true?

First note that it's not stated that x and y are integers or positive/negative.

Generally, the expression 3x/y is always prime in two cases:

When x is a multiple of prime and y is same multiple of three: x=pn and y=3n (p prime >2, n ANY number but 1), so we have 3(pn)/3n=p.

AND

When x=y ≠1 then 3x/y=3=p>2

Note that first formula also gives us the p=3 but only when x and y are the multiples of three (n ANY number but 1, can be -6 or 75 but not 1), thus it exclude all possibilities when x=y and ARE not multiples of three, for instance x=8 and y=8.

So from above it's not necessary x=y or y=1 or x,y to be primes.

Let's look:

I. x = y --> not necessarily true: x=25 y=15 3x/y=5

II. y=1 --> not necessarily true: x=8 y=8 3x/y=3

III. x and y are prime integers --> x=21 y=9 3x/y=7
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Re: PS Number property [#permalink]  13 Oct 2009, 05:18
Bunuel wrote:
If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?
Ⅰ. x = y
Ⅱ. y = 1
Ⅲ. x and y are prime integers.
(A) None
(B) Ⅰ only
(C) Ⅱonly
(D) Ⅲonly
(E) Ⅰand Ⅲ

Answer to this question is A. None of the statements (I,II,III) must be true.

This Q. can be solved by number plugging in a minute but it's quite tricky, so let's generalize it so to understand the concept, as there are many similar problems in GMAT:

Q. says that: y≠3 and that 3x/y IS a prime integer. Then it asks which of the statements MUST be true?

First note that it's not stated that x and y are integers or positive/negative.

Generally, the expression 3x/y is always prime in two cases:

When x is a multiple of prime and y is same multiple of three: x=pn and y=3n (p prime >2, n ANY number but 1), so we have 3(pn)/3n=p.

AND

When x=y ≠1 then 3x/y=3=p>2

Note that first formula also gives us the p=3 but only when x and y are the multiples of three (n ANY number but 1, can be -6 or 75 but not 1), thus it exclude all possibilities when x=y and ARE not multiples of three, for instance x=8 and y=8.

So from above it's not necessary x=y or y=1 or x,y to be primes.

Let's look:

I. x = y --> not necessarily true: x=25 y=15 3x/y=5

II. y=1 --> not necessarily true: x=8 y=8 3x/y=3

III. x and y are prime integers --> x=21 y=9 3x/y=7

can we not take fractions for x and y? The question doesnt explicitly mention them to be integers
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Re: PS Number property [#permalink]  13 Oct 2009, 11:55
I got A picking x=16 and y=6..we get 3x/y = 7....thus OA A
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Number properties: [#permalink]  07 Jun 2010, 01:11
If y ≠ 3 and is a prime integer greater than 2, which of the following must be true?
Ⅰ. x = y
Ⅱ. y = 1
Ⅲ. x and y are prime integers.
(A) None
(B) Ⅰ only
(C) Ⅱonly
(D) Ⅲonly
(E) Ⅰand Ⅲ

[Reveal] Spoiler:
A
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Re: Number properties: [#permalink]  07 Jun 2010, 04:23
I'm assuming that the question reads ... and x is a prime integer greater than 2.

III. x and y are prime integers.
Well x is a prime integer. But y could be any number other than 3. NOT TRUE.

II. y = 1. Need not be true. y could be anything other than 3.

I. x = y. Need not be true. y could be anything other than 3.

Pick A

Rather basic question, doubt you'll see this in the actual test.
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PS section 1 q20 [#permalink]  08 Jun 2010, 11:33
20. If y ≠ 3 and is a prime integer greater than 2, which of the following must be true?
Ⅰ. x = y
Ⅱ. y = 1
Ⅲ. x and y are prime integers.
(A) None
(B) Ⅰ only
(C) Ⅱonly
(D) Ⅲonly
(E) Ⅰand Ⅲ

the solution booklet says answer is A
but shouldnt x=y making B the answer
if the number is prime and greater than 2, then the number has to be 3. which is possible only if x=y.
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Re: PS section 1 q20 [#permalink]  08 Jun 2010, 12:28
sunland wrote:
20. If y ≠ 3 and is a prime integer greater than 2, which of the following must be true?
Ⅰ. x = y
Ⅱ. y = 1
Ⅲ. x and y are prime integers.
(A) None
(B) Ⅰ only
(C) Ⅱonly
(D) Ⅲonly
(E) Ⅰand Ⅲ

the solution booklet says answer is A
but shouldnt x=y making B the answer
if the number is prime and greater than 2, then the number has to be 3. which is possible only if x=y.

First of all the question misses important part (\frac{3x}{y}=prime). Second this question is MUST be true question not COULD be true.

Refer to the solutions above to see that it's not necessary x=y to be true for 3x/y to be a prime integer greater than 2. For example x=25 and y=15 --> \frac{3x}{y}=5=prime.

Hope it's clear.
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Re: PS Number property [#permalink]  01 Aug 2011, 00:38
Except for A, the rest I just need to determine the other two which one is prime number

SMAbbas wrote:
(3x/y) is a prime integer greater than 2. which of the following must be true

Suppose P=3x/y

Possible values of P = 3,5,7,11 ......

Statement I:
If P = 3 , x=y TRUE
If P = 5, x=y FALSE <== Statement I is not always correct

Statement II:
If y=1 is TRUE => P = 3x
Since P is a prime number, it cannot be a multiple of 3

Statement III:
suppose x = 7 and y=5 , P= 21/5 => Not a prime number
You can fill some other values of x and y

Re: PS Number property   [#permalink] 01 Aug 2011, 00:38
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